pls: Fit Partial Least Squares Structural Equation Models

In plssem: Complex Partial Least Squares Structural Equation Modeling

Fit Partial Least Squares Structural Equation Models

Description

pls() estimates Partial Least Squares Structural Equation Models (PLS-SEM) and their consistent (PLSc) variants. The function accepts lavaan-style syntax, handles ordered indicators through polychoric correlations and probit factor scores, and supports multilevel specifications expressed with lme4-style random effects terms inside the structural model.

Usage

pls(
  syntax,
  data,
  standardize = TRUE,
  consistent = TRUE,
  bootstrap = FALSE,
  ordered = NULL,
  missing = c("listwise", "mean", "kNN"),
  knn.k = 5,
  mcpls = NULL,
  mc.fast.lmer = mcpls,
  probit = NULL,
  tolerance = 1e-05,
  max.iter.0_5 = 500L,
  boot.ncores = 1L,
  boot.ncpus = NULL,
  boot.parallel = c("no", "multicore", "multisession", "snow"),
  boot.R = 500L,
  boot.iseed = NULL,
  sample = NULL,
  mc.min.iter = 50L,
  mc.max.iter = 1000L,
  mc.reps = 20000L,
  mc.fixed.seed = FALSE,
  mc.polyak.juditsky = TRUE,
  mc.pj.extrapolate = TRUE,
  mc.tol = if (mc.polyak.juditsky) 1e-04 else 0.001,
  mc.delta.se = TRUE,
  mc.delta.jacobian.k = max(floor(boot.R/100L), 1),
  mc.fn.args = list(),
  mc.rescov = c("auto", "reduced", "full"),
  mc.diag.secant = FALSE,
  mc.small.sample = FALSE,
  mc.small.sample.max.k = 100L,
  mc.small.sample.point.estimate = c("median", "mean"),
  verbose = interactive(),
  boot.optimize = TRUE,
  boot.drop.inadmissible = FALSE,
  mc.boot.control = list(min.iter = mc.min.iter, max.iter = mc.max.iter, mc.reps =
    floor(0.5 * mc.reps), tol = mc.tol, polyak.juditsky = mc.polyak.juditsky,
    pj.extrapolate = FALSE, verbose = FALSE, fixed.seed = TRUE, reuse.p.start = TRUE),
  reliabilities = NULL,
  default.path.estimator = c("ols", "gls"),
  ...
)

Arguments

syntax	Character string with lavaan-style model syntax describing both measurement (=~) and structural (~) relations. Random effects are specified with (term | cluster) statements.
data	A data.frame or coercible object containing the manifest indicators referenced in syntax. Ordered factors are automatically detected, but can also be supplied explicitly through ordered.
standardize	Logical; if TRUE, indicators are standardized before estimation so that factor scores have comparable scales.
consistent	Logical; TRUE requests PLSc corrections, whereas FALSE fits the traditional PLS model.
bootstrap	Logical; if TRUE, nonparametric bootstrap standard errors are computed with boot.R resamples.
ordered	Optional character vector naming manifest indicators that should be treated as ordered when computing polychoric correlations.
missing	Character string specifying how to handle missing indicator data. "listwise" removes rows with missing values (listwise deletion). "mean" imputes missing indicator values using simple univariate imputation: the mean for continuous variables, the median for ordered variables with more than two categories, and the mode for binary ordered variables (two categories) or nominal variables. "kNN" (or "knn") imputes missing indicator values using k-nearest neighbors imputation (kNN). When missing = "kNN", rows with all indicators missing are removed prior to imputation, and rows with missing cluster values are removed for multilevel models.
knn.k	Integer specifying the number of neighbors (k) used when missing = "kNN".
mcpls	Should the model be estimated using the Monte-Carlo Consistent Partial Least Squares (MC-PLSc) algorithm?
mc.fast.lmer	Should a faster (biased) GLS based estimator of the Mixed-Effects model be used in conjunction with the MC-PLS algorithm?
probit	Logical; overrides the automatic choice of probit factor scores that is based on whether ordered indicators are present.
tolerance	Numeric; Convergence criteria/tolerance.
max.iter.0_5	Maximum number of PLS iterations performed when estimating the measurement and structural models.
boot.ncores	Integer: number of workers to be used for parallel bootstrapping. Parallel bootstrapping is enabled when boot.ncores > 1.
boot.ncpus	Deprecated alias for boot.ncores.
boot.parallel	The type of parallel operation to be used (if any). The default is "no". "multisession" runs the bootstrap using multiple background R sessions (works on all platforms), while "multicore" uses forked processes (not available on Windows). "snow" is kept for backwards compatibility and is treated as an alias for "multisession". Internally this is implemented using the future package
boot.R	Integer giving the number of bootstrap resamples drawn when bootstrap = TRUE.
boot.iseed	An integer to set the bootstrap seed. Or NULL if no reproducible results are needed. This works for both serial and parallel settings. When boot.iseed is not NULL, .Random.seed (if it exists) in the global environment is left untouched.
sample	DEPRECATED. Integer giving the number of bootstrap resamples drawn when bootstrap = TRUE.
mc.min.iter	Minimum number of iterations in MC-PLS algorithm.
mc.max.iter	Maximum number of iterations in MC-PLS algorithm.
mc.reps	Monte-Carlo sample size in MC-PLS algorithm.
mc.fixed.seed	Should a fixed seed be used in the MC-PLS algorithm? Setting a fixed seed will likely yield less accurate estimates, but can substantially improve the stability and computational efficiency of the algorithm.
mc.polyak.juditsky	Should the polyak.juditsky running average method be applied in the MC-PLS algorithm?
mc.pj.extrapolate	Logical; if TRUE (the default), the Polyak-Juditsky convergence point is estimated via NLS exponential extrapolation (with Aitken \delta^2 as a fallback). If FALSE a warm start is performed instead, and the plain Polyak-Juditsky average is used. Only relevant when mc.polyak.juditsky = TRUE.
mc.tol	Tolerance in MC-PLS algorithm.
mc.delta.se	Should delta-method standard errors be computed for MC-PLS estimates?
mc.delta.jacobian.k	Integer number of Monte-Carlo Jacobians to average when computing delta-method standard errors. Defaults to one per 100 bootstrap resamples, with a minimum of 1.
mc.fn.args	Additional arguments to MC-PLS algorithm, mainly for controlling the step size.
mc.rescov	How residual covariances are treated in MC-PLS. One of "auto" (the default), "reduced", or "full". In "reduced" mode residual covariances are not treated as free parameters; they are identified from the rest of the structural model and the disturbances are simulated independently. In "full" mode the endogenous residual covariances (eta ~~ eta and xi ~~ eta) are free parameters, explicitly simulated. "auto" uses "full" when the structural model is estimated by GLS (i.e. the model contains residual covariances) and "reduced" otherwise.
mc.diag.secant	Logical; if TRUE, the MC-PLS root-finding algorithm uses a per-coordinate diagonal-secant step (estimating each coordinate's local slope from consecutive iterates), instead of the standard Robbins-Monro step. This might be usefull if the binding funtion is non-monotone.
mc.small.sample	Logical; if TRUE, average MC-PLS estimating equations over simulated samples of the observed sample size. If FALSE (default), fit one sample using all simulated observations. This assumes that the auxiliary estimator (i.e., traditional PLS) has negligible finite sample bias. I.e., that the bias of the estimator is not affected by the sample size.
mc.small.sample.max.k	Maximum number of simulated samples to average when mc.small.sample = TRUE. Defaults to 100. The number of samples is also limited by mc.reps, rounded down to a multiple of the observed sample size, with at least one sample.
mc.small.sample.point.estimate	Which point estimate of the simulated auxiliary parameters the root equation matches to the observed ones, when mc.small.sample = TRUE? "mean" solves E[\theta^{*}|\theta] = \hat{\theta}^{*}. "median" (the default) solves median[\theta^{*}|\theta] = \hat{\theta}^{*}. The median commutes with the (monotone) binding function where the mean does not, so median-matching targets a median-unbiased estimator. This removes the finite-sample bias. which can be introduced by the curvature size models, and when the indicators are uninformative (small loadings, few categories, strongly assymetric thresholds). It makes the estimating function somewhat noisier for a given number of simulated samples. Ignored when mc.small.sample = FALSE.
verbose	Should verbose output be printed?
boot.optimize	Logical; if TRUE and bootstrap = TRUE, applies the settings in mc.boot.control inside each bootstrap replicate (MC-PLS only). In general it will lead to slightly larger and less accurate standard errors.
boot.drop.inadmissible	Logical; if TRUE and bootstrap = TRUE, bootstrap replicates that yield an inadmissible solution (e.g. a Heywood case) are discarded before computing standard errors, just like replicates where the estimation procedure fails outright. Defaults to FALSE, which keeps inadmissible replicates. In either case the number of inadmissible replicates is reported. Note that dropping inadmissible solutions conditions the bootstrap distribution on well-behaved resamples and may bias the standard errors downward.
mc.boot.control	List of control parameters passed to the MC-PLS algorithm inside each bootstrap replicate when boot.optimize = TRUE.
reliabilities	Optional named numeric vector of user-supplied reliabilities used for the PLSc consistency correction.
default.path.estimator	Character string selecting the estimator used for the structural (path) model when the model does not require Generalized Least Squares (GLS). The default "ols" uses Ordinary Least Squares whenever possible, falling back to GLS automatically when the model contains residual covariances. Setting default.path.estimator = "gls" forces GLS estimation of the structural model even when OLS would otherwise be used.
...	Internal arguments. For advanced users only.

Value

A Plssem object containing the estimated parameters, fit measures, factor scores, and any bootstrap results. Methods such as summary(), coef(), and parameter_estimates() can be applied to inspect the fit.

See Also

summary, show

Examples

library(plssem)
library(modsem)

tpb <- '
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
'

fit <- pls(tpb, TPB, bootstrap = TRUE)
summary(fit)

plssem documentation built on Sept. 26, 2026, 5:06 p.m.